Geology Reference
In-Depth Information
REFRESHING PRELIMINARY ALGEBRA
AND MATHEMATICS
A few equations and expressions are reproduced below for refreshing and
their applications in later part of the theory.
/
2
xy
0
2
2
=
xy y
2
(5)
2
/
0
22
22
Similarly
=
(6)
ax
by
ax
by
2
abxy
Let us substitute
x
1
for
x
and
x
2
for
y
in the equation (5).
2
/
0
2
2
=
(7)
xx
xx xx
2
1
2
1
2
1
2
Let us substitute
1
,
2
,
x
1
,
x
2
for
a
,
b
,
x
and
y
respectively in the equation
(6).
/
0
2
22
22
=
(8)
Then
x
x
x
2
x x
x
11
2 2
11
1212
22
2
)
x
(
1
x
1
+
'
2
x
2
) can be written in the form of =
(9)
ii
i
1
22
))
xx
/
0
2
22
22
Then
x
x
=
x
x
2
x x
=
(10)
ijij
11
2 2
11
22
1212
i
11
j
This is because in the equation (10), when
i
=
j
= 1 the resulting term is
2
x
2
; and when
i
= 1,
j
= 2 the term is
1
2
x
1
x
2
. Similarly when
i
= 2,
j
= 1 the term
2
1
x
1
x
2
results.
Therefore, equation (10) can also be written as
2
2
1
x
1
; when
i
=
j
= 2 the term is
2
)
)
)
x
xx
xx
=
(11)
ii
ijij
ijij
i
ji
i j
1
The above formula can be simplified and written as
2
)
x
))
=
xx
(12)
ii
ijij
i
i
j
This is an important derivation. Generally one is prone to confusion as to
how the terms with
j
have come, when it is not there originally. This formula
has got extensive application in statistics and geostatistics.
PROBLEM OF CALCULATING MEAN AND
CONCEPT OF VARIOGRAM
Let us summarize again the most common statistics and their forms used in
the development of geostatistical methods.
